Partial differential equations stand as fundamental tools in understanding the dynamic behavior and allow us to predict trends. Therefore, solving these equations becomes essential for research purposes. In particular, approximations are used to solve complex and challenging equations, among which Finite Element Method (FEM) is prominent. In FEM, the target domain is discretized into finite elements numerically, known as discretization, to get an unknown solution vector. A finer grid, which allows for smoother outcomes, requires significant computational effort and huge memory resources. While the advent of computers and advances in chip integration, along with the development of parallel computing, have increased the feasibility of computation, efficient resource utilization has become a pressing challenge to save time and energy. Therefore, we focus on the study of the Overlapping Domain Decomposition method. Originating from H.A.Schwarz’s idea in the 19th century, this method divides a global domain into overlapped subdomains and solves them separately with Dirichlet boundary conditions only at the boundary. It has been shown to yield solutions to the Poisson equation. We aim to implement this method using FEM for parallel computing, evaluating accuracy and performance. For the implementation, the DUNE toolbox was used and measurements were performed on the Barnard cluster.